Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models

Firing rate models for gamma oscillations in I-I and E-I networks

Firing rate models for describing the mean-field activities of neuronal ensembles can be used effectively to study network function and dynamics, including synchronization and rhythmicity of excitatory-inhibitory populations. However, traditional Wilson-Cowan-like models, even when extended to include an explicit dynamic synaptic activation variable, are found unable to capture some dynamics such as Interneuronal Network Gamma oscillations (ING). Use of an explicit delay is helpful in simulations at the expense of complicating mathematical analysis. We resolve this issue by introducing a dynamic variable, u, that acts as an effective delay in the negative feedback loop between firing rate (r) and synaptic gating of inhibition (s). In effect, u endows synaptic activation with second order dynamics. With linear stability analysis, numerical branch-tracking and simulations, we show that our r-u-s rate model captures some key qualitative features of spiking network models for ING. We also propose an alternative formulation, a v-u-s model, in which mean membrane potential v satisfies an averaged current-balance equation. Furthermore, we extend the framework to E-I networks. With our six-variable v-u-s model, we demonstrate in firing rate models the transition from Pyramidal-Interneuronal Network Gamma (PING) to ING by increasing the external drive to the inhibitory population without adjusting synaptic weights. Having PING and ING available in a single network, without invoking synaptic blockers, is plausible and natural for explaining the emergence and transition of two different types of gamma oscillations.

Neurophysiological avenues to better conceptualizing adaptive cognition

We delve into the human brain's remarkable capacity for adaptability and sustained cognitive functioning, phenomena traditionally encompassed as executive functions or cognitive control. The neural underpinnings that enable the seamless navigation between transient thoughts without detracting from overarching goals form the core of our article. We discuss the concept of "metacontrol," which builds upon conventional cognitive control theories by proposing a dynamic balancing of processes depending on situational demands. We critically discuss the role of oscillatory processes in electrophysiological activity at different scales and the importance of desynchronization and partial phase synchronization in supporting adaptive behavior including neural noise accounts, transient dynamics, phase-based measures (coordination dynamics) and neural mass modelling. The cognitive processes focused and neurophysiological avenues outlined are integral to understanding diverse psychiatric disorders thereby contributing to a more nuanced comprehension of cognitive control and its neural bases in both health and disease.

Analysis of hippocampal local field potentials by diffusion mapped delay coordinates

Spatial navigation through novel spaces and to known goal locations recruits multiple integrated structures in the mammalian brain. Within this extended network, the hippocampus enables formation and retrieval of cognitive spatial maps and contributes to decision making at choice points. Exploration and navigation to known goal locations produce synchronous activity of hippocampal neurons resulting in rhythmic oscillation events in local networks. Power of specific oscillatory frequencies and numbers of these events recorded in local field potentials correlate with distinct cognitive aspects of spatial navigation. Typically, oscillatory power in brain circuits is analyzed with Fourier transforms or short-time Fourier methods, which involve assumptions about the signal that are likely not true and fail to succinctly capture potentially informative features. To avoid such assumptions, we applied a method that combines manifold discovery techniques with dynamical systems theory, namely diffusion maps and Takens' time-delay embedding theory, that avoids limitations seen in traditional methods. This method, called diffusion mapped delay coordinates (DMDC), when applied to hippocampal signals recorded from juvenile rats freely navigating a Y-maze, replicates some outcomes seen with standard approaches and identifies age differences in dynamic states that traditional analyses are unable to detect. Thus, DMDC may serve as a suitable complement to more traditional analyses of LFPs recorded from behaving subjects that may enhance information yield.

A dynamical computational model of theta generation in hippocampal circuits to study theta-gamma oscillations during neurostimulation

Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear. In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity. Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive. We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations. Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations. Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations. This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.

Examining the low-voltage fast seizure-onset and its response to optogenetic stimulation in a biophysical network model of the hippocampus

Low-voltage fast (LVF) seizure-onset is one of the two frequently observed temporal lobe seizure-onset patterns. Depth electroencephalogram profile analysis illustrated that the peak amplitude of LVF onset was deep temporal areas, e.g., hippocampus. However, the specific dynamic transition mechanisms between normal hippocampal rhythmic activity and LVF seizure-onset remain unclear. Recently, the optogenetic approach to gain control over epileptic hyper-excitability both in vitro and in vivo has become a novel noninvasive modulation strategy. Here, we combined biophysical modeling to study LVF dynamics following changes in crucial physiological parameters, and investigated the potential optogenetic intervention mechanism for both excitatory and inhibitory control. In an Ammon's horn 3 (CA3) biophysical model with light-sensitive protein channelrhodopsin 2 (ChR2), we found that the cooperative effects of excessive extracellular potassium concentration of parvalbumin-positive (PV+) inhibitory interneurons and synaptic links could induce abundant types of discharges of the hippocampus, and lead to transitions from gamma oscillations to LVF seizure-onset. Simulations of optogenetic stimulation revealed that the LVF seizure-onset and morbid fast spiking could not be eliminated by targeting PV+ neurons, whereas the epileptic network was more sensitive to the excitatory control of principal neurons with strong optogenetic currents. We illustrate that in the epileptic hippocampal network, the trajectories of the normal and the seizure state are in close vicinity and optogenetic perturbations therefore may result in transitions. The network model system developed in this study represents a scientific instrument to disclose the underlying principles of LVF, to characterize the effects of optogenetic neuromodulation, and to guide future treatment for specific types of seizures.

Exact low-dimensional description for fast neural oscillations with low firing rates

Recently, low-dimensional models of neuronal activity have been exactly derived for large networks of deterministic, quadratic integrate-and-fire (QIF) neurons. Such firing rate models (FRM) describe the emergence of fast collective oscillations (>30 Hz) via the frequency locking of a subset of neurons to the global oscillation frequency. However, the suitability of such models to describe realistic neuronal states is seriously challenged by the fact that during episodes of fast collective oscillations, neuronal discharges are often very irregular and have low firing rates compared to the global oscillation frequency. Here we extend the theory to derive exact FRM for QIF neurons to include noise and show that networks of stochastic neurons displaying irregular discharges at low firing rates during episodes of fast oscillations are governed by exactly the same evolution equations as deterministic networks. Our results reconcile two traditionally confronted views on neuronal synchronization and upgrade the applicability of exact FRM to describe a broad range of biologically realistic neuronal states.

Data-driven modelling of brain activity using neural networks, diffusion maps, and the Koopman operator

We propose a machine-learning approach to construct reduced-order models (ROMs) to predict the long-term out-of-sample dynamics of brain activity (and in general, high-dimensional time series), focusing mainly on task-dependent high-dimensional fMRI time series. Our approach is a three stage one. First, we exploit manifold learning and, in particular, diffusion maps (DMs) to discover a set of variables that parametrize the latent space on which the emergent high-dimensional fMRI time series evolve. Then, we construct ROMs on the embedded manifold via two techniques: Feedforward Neural Networks (FNNs) and the Koopman operator. Finally, for predicting the out-of-sample long-term dynamics of brain activity in the ambient fMRI space, we solve the pre-image problem, i.e., the construction of a map from the low-dimensional manifold to the original high-dimensional (ambient) space by coupling DMs with Geometric Harmonics (GH) when using FNNs and the Koopman modes per se. For our illustrations, we have assessed the performance of the two proposed schemes using two benchmark fMRI time series: (i) a simplistic five-dimensional model of stochastic discrete-time equations used just for a "transparent" illustration of the approach, thus knowing a priori what one expects to get, and (ii) a real fMRI dataset with recordings during a visuomotor task. We show that the proposed Koopman operator approach provides, for any practical purposes, equivalent results to the FNN-GH approach, thus bypassing the need to train a non-linear map and to use GH to extrapolate predictions in the ambient space; one can use instead the low-frequency truncation of the DMs function space of L2-integrable functions to predict the entire list of coordinate functions in the ambient space and to solve the pre-image problem.

Periodic solutions in next generation neural field models

We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic solutions. Using the fact that the dynamics at each spatial location are described by a complex-valued Riccati equation we derive a self-consistency equation that such periodic solutions must satisfy. We determine the stability of these solutions, and present numerical results to illustrate the usefulness of this technique. The generality of this approach is demonstrated through its application to several other systems involving delays, two-population architecture and networks of Winfree oscillators.

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.

Constructive role of shot noise in the collective dynamics of neural networks

Finite-size effects may significantly influence the collective dynamics of large populations of neurons. Recently, we have shown that in globally coupled networks these effects can be interpreted as additional common noise term, the so-called shot noise, to the macroscopic dynamics unfolding in the thermodynamic limit. Here, we continue to explore the role of the shot noise in the collective dynamics of globally coupled neural networks. Namely, we study the noise-induced switching between different macroscopic regimes. We show that shot noise can turn attractors of the infinitely large network into metastable states whose lifetimes smoothly depend on the system parameters. A surprising effect is that the shot noise modifies the region where a certain macroscopic regime exists compared to the thermodynamic limit. This may be interpreted as a constructive role of the shot noise since a certain macroscopic state appears in a parameter region where it does not exist in an infinite network.

Multi-band oscillations emerge from a simple spiking network

In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8-12 Hz), beta (12.5-30 Hz), and gamma (30-120 Hz) oscillations, among others. These rhythms are believed to underlie information processing and cognitive functions and have been subjected to intense experimental and theoretical scrutiny. Computational modeling has provided a framework for the emergence of network-level oscillatory behavior from the interaction of spiking neurons. However, due to the strong nonlinear interactions between highly recurrent spiking populations, the interplay between cortical rhythms in multiple frequency bands has rarely been theoretically investigated. Many studies invoke multiple physiological timescales (e.g., various ion channels or multiple types of inhibitory neurons) or oscillatory inputs to produce rhythms in multi-bands. Here, we demonstrate the emergence of multi-band oscillations in a simple network consisting of one excitatory and one inhibitory neuronal population driven by constant input. First, we construct a data-driven, Poincaré section theory for robust numerical observations of single-frequency oscillations bifurcating into multiple bands. Then, we develop model reductions of the stochastic, nonlinear, high-dimensional neuronal network to capture the appearance of multi-band dynamics and the underlying bifurcations theoretically. Furthermore, when viewed within the reduced state space, our analysis reveals conserved geometrical features of the bifurcations on low-dimensional dynamical manifolds. These results suggest a simple geometric mechanism behind the emergence of multi-band oscillations without appealing to oscillatory inputs or multiple synaptic or neuronal timescales. Thus, our work points to unexplored regimes of stochastic competition between excitation and inhibition behind the generation of dynamic, patterned neuronal activities.

Transient gamma events delineate somatosensory modality in S1

Gamma band activity localized to the primary somatosensory cortex (S1) in humans and animals is implicated in the higher order neural processing of painful and tactile stimuli. However, it is unclear if gamma band activity differs between these distinct somatosensory modalities. Here, we coupled a novel behavioral approach with chronic extracellular electrophysiology to investigate differences in S1 gamma band activity elicited by noxious and innocuous hind paw stimulation in transgenic mice. Like prior studies, we found that trial-averaged gamma power in S1 increased following both noxious and innocuous stimuli. However, on individual trials, we noticed that evoked gamma band activity was not a continuous oscillatory signal but a series of transient spectral events. Upon further analysis we found that there was a significantly higher incidence of these gamma band events following noxious stimulation than innocuous stimulation. These findings suggest that somatosensory stimuli may be represented by specific features of gamma band activity at the single trial level, which may provide insight to mechanisms underlying acute pain.

Theta-gamma phase amplitude coupling in a hippocampal CA1 microcircuit

Phase amplitude coupling (PAC) between slow and fast oscillations is found throughout the brain and plays important functional roles. Its neural origin remains unclear. Experimental findings are often puzzling and sometimes contradictory. Most computational models rely on pairs of pacemaker neurons or neural populations tuned at different frequencies to produce PAC. Here, using a data-driven model of a hippocampal microcircuit, we demonstrate that PAC can naturally emerge from a single feedback mechanism involving an inhibitory and excitatory neuron population, which interplay to generate theta frequency periodic bursts of higher frequency gamma. The model suggests the conditions under which a CA1 microcircuit can operate to elicit theta-gamma PAC, and highlights the modulatory role of OLM and PVBC cells, recurrent connectivity, and short term synaptic plasticity. Surprisingly, the results suggest the experimentally testable prediction that the generation of the slow population oscillation requires the fast one and cannot occur without it.

Population spiking and bursting in next-generation neural masses with spike-frequency adaptation

Spike-frequency adaptation (SFA) is a fundamental neuronal mechanism taking into account the fatigue due to spike emissions and the consequent reduction of the firing activity. We have studied the effect of this adaptation mechanism on the macroscopic dynamics of excitatory and inhibitory networks of quadratic integrate-and-fire (QIF) neurons coupled via exponentially decaying post-synaptic potentials. In particular, we have studied the population activities by employing an exact mean-field reduction, which gives rise to next-generation neural mass models. This low-dimensional reduction allows for the derivation of bifurcation diagrams and the identification of the possible macroscopic regimes emerging both in a single and in two identically coupled neural masses. In single populations SFA favors the emergence of population bursts in excitatory networks, while it hinders tonic population spiking for inhibitory ones. The symmetric coupling of two neural masses, in absence of adaptation, leads to the emergence of macroscopic solutions with broken symmetry, namely, chimera-like solutions in the inhibitory case and antiphase population spikes in the excitatory one. The addition of SFA leads to new collective dynamical regimes exhibiting cross-frequency coupling (CFC) among the fast synaptic timescale and the slow adaptation one, ranging from antiphase slow-fast nested oscillations to symmetric and asymmetric bursting phenomena. The analysis of these CFC rhythms in the θ-γ range has revealed that a reduction of SFA leads to an increase of the θ frequency joined to a decrease of the γ one. This is analogous to what has been reported experimentally for the hippocampus and the olfactory cortex of rodents under cholinergic modulation, which is known to reduce SFA.

Neuroprosthetics: from sensorimotor to cognitive disorders

Neuroprosthetics is a multidisciplinary field at the interface between neurosciences and biomedical engineering, which aims at replacing or modulating parts of the nervous system that get disrupted in neurological disorders or after injury. Although neuroprostheses have steadily evolved over the past 60 years in the field of sensory and motor disorders, their application to higher-order cognitive functions is still at a relatively preliminary stage. Nevertheless, a recent series of proof-of-concept studies suggest that electrical neuromodulation strategies might also be useful in alleviating some cognitive and memory deficits, in particular in the context of dementia. Here, we review the evolution of neuroprosthetics from sensorimotor to cognitive disorders, highlighting important common principles such as the need for neuroprosthetic systems that enable multisite bidirectional interactions with the nervous system.

A multi-scale model explains oscillatory slowing and neuronal hyperactivity in Alzheimer's disease

Alzheimer's disease is the most common cause of dementia and is linked to the spreading of pathological amyloid-β and tau proteins throughout the brain. Recent studies have highlighted stark differences in how amyloid-β and tau affect neurons at the cellular scale. On a larger scale, Alzheimer's patients are observed to undergo a period of early-stage neuronal hyperactivation followed by neurodegeneration and frequency slowing of neuronal oscillations. Herein, we model the spreading of both amyloid-β and tau across a human connectome and investigate how the neuronal dynamics are affected by disease progression. By including the effects of both amyloid-β and tau pathology, we find that our model explains AD-related frequency slowing, early-stage hyperactivation and late-stage hypoactivation. By testing different hypotheses, we show that hyperactivation and frequency slowing are not due to the topological interactions between different regions but are mostly the result of local neurotoxicity induced by amyloid-β and tau protein.

Shot noise in next-generation neural mass models for finite-size networks

Neural mass models is a general name for various models describing the collective dynamics of large neural populations in terms of averaged macroscopic variables. Recently, the so-called next-generation neural mass models have attracted a lot of attention due to their ability to account for the degree of synchrony. Being exact in the limit of infinitely large number of neurons, these models provide only an approximate description of finite-size networks. In the present Letter we study finite-size effects in the collective behavior of neural networks and prove that these effects can be captured by appropriately modified neural mass models. Namely, we show that the finite size of the network leads to the emergence of the so-called shot noise appearing as a stochastic term in the neural mass model. The power spectrum of this shot noise contains pronounced peaks, therefore its impact on the collective dynamics might be crucial due to resonance effects.

Interneuronal network model of theta-nested fast oscillations predicts differential effects of heterogeneity, gap junctions and short term depression for hyperpolarizing versus shunting inhibition

Theta and gamma oscillations in the hippocampus have been hypothesized to play a role in the encoding and retrieval of memories. Recently, it was shown that an intrinsic fast gamma mechanism in medial entorhinal cortex can be recruited by optogenetic stimulation at theta frequencies, which can persist with fast excitatory synaptic transmission blocked, suggesting a contribution of interneuronal network gamma (ING). We calibrated the passive and active properties of a 100-neuron model network to capture the range of passive properties and frequency/current relationships of experimentally recorded PV+ neurons in the medial entorhinal cortex (mEC). The strength and probabilities of chemical and electrical synapses were also calibrated using paired recordings, as were the kinetics and short-term depression (STD) of the chemical synapses. Gap junctions that contribute a noticeable fraction of the input resistance were required for synchrony with hyperpolarizing inhibition; these networks exhibited theta-nested high frequency oscillations similar to the putative ING observed experimentally in the optogenetically-driven PV-ChR2 mice. With STD included in the model, the network desynchronized at frequencies above ~200 Hz, so for sufficiently strong drive, fast oscillations were only observed before the peak of the theta. Because hyperpolarizing synapses provide a synchronizing drive that contributes to robustness in the presence of heterogeneity, synchronization decreases as the hyperpolarizing inhibition becomes weaker. In contrast, networks with shunting inhibition required non-physiological levels of gap junctions to synchronize using conduction delays within the measured range.

Development of Mechanistic Neural Mass (mNM) Models that Link Physiology to Mean-Field Dynamics

Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities-termed neural masses-to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson's disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.

Mean-field equations for neural populations with q-Gaussian heterogeneities

Describing the collective dynamics of large neural populations using low-dimensional models for averaged variables has long been an attractive task in theoretical neuroscience. Recently developed reduction methods make it possible to derive such models directly from the microscopic dynamics of individual neurons. To simplify the reduction, the Cauchy distribution is usually assumed for heterogeneous network parameters. Here we extend the reduction method for a wider class of heterogeneities defined by the q-Gaussian distribution. The shape of this distribution depends on the Tsallis index q and gradually changes from the Cauchy distribution to the normal Gaussian distribution as this index changes. We derive the mean-field equations for an inhibitory network of quadratic integrate-and-fire neurons with a q-Gaussian-distributed excitability parameter. It is shown that the dynamic modes of the network significantly depend on the form of the distribution determined by the Tsallis index. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.

Cortical Cross-Frequency Coupling Is Affected by in utero Exposure to Antidepressant Medication

Up to five percent of human infants are exposed to maternal antidepressant medication by serotonin reuptake inhibitors (SRI) during pregnancy, yet the SRI effects on infants’ early neurodevelopment are not fully understood. Here, we studied how maternal SRI medication affects cortical frequency-specific and cross-frequency interactions estimated, respectively, by phase-phase correlations (PPC) and phase-amplitude coupling (PAC) in electroencephalographic (EEG) recordings. We examined the cortical activity in infants after fetal exposure to SRIs relative to a control group of infants without medical history of any kind. Our findings show that the sleep-related dynamics of PPC networks are selectively affected by in utero SRI exposure, however, those alterations do not correlate to later neurocognitive development as tested by neuropsychological evaluation at two years of age. In turn, phase-amplitude coupling was found to be suppressed in SRI infants across multiple distributed cortical regions and these effects were linked to their neurocognitive outcomes. Our results are compatible with the overall notion that in utero drug exposures may cause subtle, yet measurable changes in the brain structure and function. Our present findings are based on the measures of local and inter-areal neuronal interactions in the cortex which can be readily used across species, as well as between different scales of inspection: from the whole animals to in vitro preparations. Therefore, this work opens a framework to explore the cellular and molecular mechanisms underlying neurodevelopmental SRI effects at all translational levels.

Connectomics of human electrophysiology

We present both a scientific overview and conceptual positions concerning the challenges and assets of electrophysiological measurements in the search for the nature and functions of the human connectome. We discuss how the field has been inspired by findings and approaches from functional magnetic resonance imaging (fMRI) and informed by a small number of significant multimodal empirical studies, which show that the canonical networks that are commonplace in fMRI are in fact rooted in electrophysiological processes. This review is also an opportunity to produce a brief, up-to-date critical survey of current data modalities and analytical methods available for deriving both static and dynamic connectomes from electrophysiology. We review hurdles that challenge the significance and impact of current electrophysiology connectome research. We then encourage the field to take a leap of faith and embrace the wealth of electrophysiological signals, despite their apparent, disconcerting complexity. Our position is that electrophysiology connectomics is poised to inform testable mechanistic models of information integration in hierarchical brain networks, constructed from observable oscillatory and aperiodic signal components and their polyrhythmic interactions.

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

Suppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons

Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We show that in the limit cycle mode, high-frequency stimulation of an inhibitory population can stabilize an unstable resting state and effectively suppress collective oscillations. We also show that in the bistable mode, the dynamics of the network can be switched from a stable limit cycle to a stable resting state by applying an inhibitory pulse to the excitatory population. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.

Reduction Methodology for Fluctuation Driven Population Dynamics

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions due to the divergence of all the moments (cumulants). We have solved this problem by introducing a "pseudocumulants" expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsic and endogenous fluctuations, thus obtaining a unified mean-field formulation encompassing quenched and dynamical sources of disorder.

Frontopolar theta oscillations link metacognition with prospective decision making

Prospective decision making considers the future consequences of actions and therefore requires agents to represent their present subjective preferences reliably across time. Here, we test the link of frontopolar theta oscillations to both metacognitive ability and prospective choice behavior. We target these oscillations with transcranial alternating current stimulation while participants make decisions between smaller-sooner and larger-later monetary rewards and rate their choice confidence after each decision. Stimulation designed to enhance frontopolar theta oscillations increases metacognitive accuracy in reports of subjective uncertainty in intertemporal decisions. Moreover, the stimulation also enhances the willingness of participants to restrict their future access to short-term gratification by strengthening the awareness of potential preference reversals. Our results suggest a mechanistic link between frontopolar theta oscillations and metacognitive knowledge about the stability of subjective value representations, providing a potential explanation for why frontopolar cortex also shields prospective decision making against future temptation.

Coherence resonance in neuronal populations: Mean-field versus network model

The counterintuitive phenomenon of coherence resonance describes a nonmonotonic behavior of the regularity of noise-induced oscillations in the excitable regime, leading to an optimal response in terms of regularity of the excited oscillations for an intermediate noise intensity. We study this phenomenon in populations of FitzHugh-Nagumo (FHN) neurons with different coupling architectures. For networks of FHN systems in an excitable regime, coherence resonance has been previously analyzed numerically. Here we focus on an analytical approach studying the mean-field limits of the globally and locally coupled populations. The mean-field limit refers to an averaged behavior of a complex network as the number of elements goes to infinity. We apply the mean-field approach to the globally coupled FHN network. Further, we derive a mean-field limit approximating the locally coupled FHN network with low noise intensities. We study the effects of the coupling strength and noise intensity on coherence resonance for both the network and the mean-field models. We compare the results of the mean-field and network frameworks and find good agreement in the globally coupled case, where the correspondence between the two approaches is sufficiently good to capture the emergence of coherence resonance, as well as of anticoherence resonance.

Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons

We study the macroscopic dynamics of large networks of excitable type 1 neurons composed of two populations interacting with disparate but symmetric intra- and inter-population coupling strengths. This nonuniform coupling scheme facilitates symmetric equilibria, where both populations display identical firing activity, characterized by either quiescent or spiking behavior, or asymmetric equilibria, where the firing activity of one population exhibits quiescent but the other exhibits spiking behavior. Oscillations in the firing rate are possible if neurons emit pulses with non-zero width but are otherwise quenched. Here, we explore how collective oscillations emerge for two statistically identical neuron populations in the limit of an infinite number of neurons. A detailed analysis reveals how collective oscillations are born and destroyed in various bifurcation scenarios and how they are organized around higher codimension bifurcation points. Since both symmetric and asymmetric equilibria display bistable behavior, a large configuration space with steady and oscillatory behavior is available. Switching between configurations of neural activity is relevant in functional processes such as working memory and the onset of collective oscillations in motor control.

Exact neural mass model for synaptic-based working memory

A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks encompassing realistic cellular mechanisms for short-term synaptic plasticity. This population model reproduces the macroscopic dynamics of the network in terms of the firing rate and the mean membrane potential. The latter quantity allows us to gain insight of the Local Field Potential and electroencephalographic signals measured during WM tasks to characterize the brain activity. More specifically synaptic facilitation and depression integrate each other to efficiently mimic WM operations via either synaptic reactivation or persistent activity. Memory access and loading are related to stimulus-locked transient oscillations followed by a steady-state activity in the β-γ band, thus resembling what is observed in the cortex during vibrotactile stimuli in humans and object recognition in monkeys. Memory juggling and competition emerge already by loading only two items. However more items can be stored in WM by considering neural architectures composed of multiple excitatory populations and a common inhibitory pool. Memory capacity depends strongly on the presentation rate of the items and it maximizes for an optimal frequency range. In particular we provide an analytic expression for the maximal memory capacity. Furthermore, the mean membrane potential turns out to be a suitable proxy to measure the memory load, analogously to event driven potentials in experiments on humans. Finally we show that the γ power increases with the number of loaded items, as reported in many experiments, while θ and β power reveal non monotonic behaviours. In particular, β and γ rhythms are crucially sustained by the inhibitory activity, while the θ rhythm is controlled by excitatory synapses.

Working Memory (WM) is the ability to temporarily store and manipulate stimuli representations that are no longer available to the senses. We have developed an innovative coarse-grained population model able to mimic several operations associated to WM. The novelty of the model consists in reproducing exactly the dynamics of spiking neural networks with realistic synaptic plasticity composed of hundreds of thousands of neurons in terms of a few macroscopic variables. These variables give access to experimentally measurable quantities such as local field potentials and electroencephalographic signals. Memory operations are joined to sustained or transient oscillations emerging in different frequency bands, in accordance with experimental results for primate and humans performing WM tasks. We have designed an architecture composed of many excitatory populations and a common inhibitory pool able to store and retain several memory items. The capacity of our multi-item architecture is around 3–5 items, a value similar to the WM capacities measured in many experiments. Furthermore, the maximal capacity is achievable only for presentation rates within an optimal frequency range. Finally, we have defined a measure of the memory load analogous to the event-related potentials employed to test humans’ WM capacity during visual memory tasks.

Exact Mean-Field Theory Explains the Dual Role of Electrical Synapses in Collective Synchronization

Electrical synapses play a major role in setting up neuronal synchronization, but the precise mechanisms whereby these synapses contribute to synchrony are subtle and remain elusive. To investigate these mechanisms mean-field theories for quadratic integrate-and-fire neurons with electrical synapses have been recently put forward. Still, the validity of these theories is controversial since they assume that the neurons produce unrealistic, symmetric spikes, ignoring the well-known impact of spike shape on synchronization. Here, we show that the assumption of symmetric spikes can be relaxed in such theories. The resulting mean-field equations reveal a dual role of electrical synapses: First, they equalize membrane potentials favoring the emergence of synchrony. Second, electrical synapses act as "virtual chemical synapses," which can be either excitatory or inhibitory depending upon the spike shape. Our results offer a precise mathematical explanation of the intricate effect of electrical synapses in collective synchronization. This reconciles previous theoretical and numerical works, and confirms the suitability of recent low-dimensional mean-field theories to investigate electrically coupled neuronal networks.

Mapping Mind-Brain Development: Towards a Comprehensive Theory

The relations between the developing mind and developing brain are explored. We outline a theory of intellectual development postulating that the mind comprises four systems of processes (domain-specific, attention and working memory, reasoning, and cognizance) developing in four cycles (episodic, realistic, rule-based, and principle-based representations, emerging at birth, 2, 6, and 11 years, respectively), with two phases in each. Changes in reasoning relate to processing efficiency in the first phase and working memory in the second phase. Awareness of mental processes is recycled with the changes in each cycle and drives their integration into the representational unit of the next cycle. Brain research shows that each type of processes is served by specialized brain networks. Domain-specific processes are rooted in sensory cortices; working memory processes are mainly rooted in hippocampal, parietal, and prefrontal cortices; abstraction and alignment processes are rooted in parietal, frontal, and prefrontal and medial cortices. Information entering these networks is available to awareness processes. Brain networks change along the four cycles, in precision, connectivity, and brain rhythms. Principles of mind-brain interaction are discussed.